Abstract
A divide-and-conquer approach for the feedback arc set is presented. The divide step is performed by solving a minimum bisection problem. Two strategies are used to solve minimum bisection problem: A heuristic based on the stochastic evolution methodology, and a heuristic based on dynamic clustering. Empirical results are presented to compare our method with other approaches. An algorithm to construct test cases for the feedback arc set problem with known optimal number of feedback arcs, is also presented.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Berger, B. and P.W. Shor. (1990). “Approximation Algorithms for the Maximum Acyclic Subgraph Problem.” In Proc. First ACM-SIAM Symp. Discrete Algorithms. pp. 236–243.
Calazans, Ney, et al. (1992). “Advanced Ordering and Manipulation Techniques for Binary Decision Diagrams.” In European Design Automation Conference, Brussels, Belgium. pp. 452–457.
Cormen, T., C. Leiserson, and R. Rivest. (1990). Introduction to Algorithms. Cambridge, Mass: The MIT Press.
De Souza, C., R. Keunings, L. Wolsey, and O. Zone. (1994). “A New Approach to Minimizing the Frontwidth in Finite Element Calculations.” Computer Methods in Applied Mechanics and Engineering 111(3/4), 323–334.
Eades, P. and X. Lin. (To appear). “AHeuristic for the Feedback Arc Set Problem.”Australasian J. of Combinatorics.
Eades, P., X. Lin, and W.F. Smyth. (1993). “A Fast and Effective Heuristic for the Feedback Arc Set Problem.” Inf. Proc. Lett. 47, 319–323.
Eades, P., W.F. Smyth, and X. Lin. (1989). “Heuristics for the Feedback Arc Set Problem.” Tech. Rept. 1, School of Computing Science, Curtin University of Technology, Perth, Western Australia.
Ford, L. and D. Fulkerson. (1962). Flows in Networks. Princeton, NJ: Princeton University Press.
Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. New York, NY: W. H. Freeman and Company.
Goldberg, A. and R. Tarjan. (1986). “A New Approach to the Maximum Flow Problem.” In Proc. Eight ACM Symp. on Theory of Computing. pp. 136–146.
Lempel, A. and I. Cederbaum. (1966). “Minimum Feedback Arc and Vertex Sets of a Directed Graph.” IEEET Trans. Circuit TheoryCT-13(4), 399–403.
Lucchesi, C.L. (1976). “A Minimax Equality For Directed Graphs.” Doctoral Thesis, University of Waterloo, Ontario, Canada.
Lucchesi, C.L. and D.H. Younger. (1978). “A Minimax Theorem For Directed Graphs.” J. London Math. Soc. 2(17), 369–374.
Mitra, B., P. Ranjan Panda, and P. Pal Chaudhuri. (1993). “Estimating the Complexity of Synthesized Designs from FSM Specifications.” IEEE Design & Test of Computers 10(1), 30–35.
Cherabuddi, Raghava V. and Magdy A. Bayoumi. (1994). “Automated System Partitioning for Synthesis of Multi-Chip Modules.” In Fourth Great Lakes Symposium on VLSI, Design Automation of High Performance VLSI Systems. pp. 21–25.
Ramachandran, V. (1988). “Finding Minimum Feedback Arc Set in Reducible Flow graphs.” J. Algorithms 9, 299–313.
Saab, Y. (1990). “Combinatorial Optimization by Stochastic Evolution with Applications to the Physical Design of VLSI Circuits”. Doctoral Thesis, University of Illinois at Urbana-Champaign.
Saab, Y. (1993). “Post-Analysis-Based Clustering Dramatically Improves the Fiduccia-Mattheyses Algorithm.” In European Design Automation Conference, Hamburg, Germany. pp. 22–27.
Saab, Y. (1995). “A Fast and Robust Network Bisection Algorithm.” IEEE Trans. Computers 44(7), 903–913.
Saab, Y. and V. Rao. (1991). “Combinatorial Optimization by Stochastic Evolution.” IEEE Trans. Computer-Aided Design 10(4), 525–535.
Seshu, S. and M.B. Reed. (1961). Linear Graphs and Electrical Networks. Reading, Mass: Addison Wesley.
Slater, P. (1971). “Optimal Ranking of Tournaments.” Networks 1, 135–138.
Unger, S.H. (1957). “A Study of Asynchronous Logical Feedback Networks.” Tech. Rept. 320, Research Lab. of Electronics, MIT, Cambridge, Mass.
Younger, D.H. (1963). “Minimum Feedback Arc Sets for a Directed Graph.” IEEE Trans. Circuit Theory CT-10, 238–245.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Saab, Y. A Fast and Effective Algorithm for the Feedback Arc Set Problem. Journal of Heuristics 7, 235–250 (2001). https://doi.org/10.1023/A:1011315014322
Issue Date:
DOI: https://doi.org/10.1023/A:1011315014322